The Ripple Tank | mysimulator.uk

One equation, every ripple

Nudge the surface of a shallow tray of water and the disturbance spreads outward as a circular ripple, governed by the same equation that describes sound in air, vibrations on a drum skin, and light in a vacuum: the wave equation. In two dimensions, with h the height of the surface above rest and c the wave speed, it reads:

d^2 h / d t^2  =  c^2 * ( d^2 h / d x^2  +  d^2 h / d y^2 )

Physically, that says the surface accelerates upward wherever it curves downward relative to its neighbours, and vice versa - a point that is lower than the average of the points around it gets pulled back up, and a point higher than average gets pulled back down. Solve that rule everywhere on a grid, step by step, and the individual pushes and pulls of every point combine into ripples travelling outward at speed c.

live demo · circular wavefronts from a point source● LIVE

Interference: waves adding and cancelling

Because the wave equation is linear, two overlapping ripples simply add together at every point - the principle of superposition. Two point sources oscillating in step produce a fixed pattern of bright rays where the ripples arrive in phase and reinforce (constructive interference) alternating with dark rays where a crest from one source meets a trough from the other and they cancel (destructive interference). This is the classic double-source ripple-tank pattern, and it is exactly the same mathematics behind Young's double-slit experiment with light and behind noise-cancelling headphones.

Diffraction: bending around the edges

Send a straight, plane wavefront at a barrier with a narrow gap and the water on the far side does not stay in a neat straight-edged shadow the way a ray of light would from a simple obstruction. Instead the opening itself behaves, by Huygens' principle, as a fresh point source radiating outward in near-circular wavefronts. The narrower the gap relative to the wavelength, the more completely the wave spreads out behind it; a gap much wider than the wavelength barely disturbs the wave's straight-line path except right at its two edges.

Refraction: bending toward the shallows

In shallow water, wave speed depends on depth:

c = sqrt(g * h)     // g = 9.81 m/s^2, h = water depth

Slide a raised shelf into the tank so the depth drops suddenly on one side, and a wave crossing that boundary at an angle slows down as soon as part of its front reaches the shallow region while the rest is still moving fast in deep water. That mismatch bends the wavefront toward the shallow side, the same refraction that bends light entering glass, and the reason ocean waves swing around to arrive almost parallel to a beach no matter what angle they started at offshore.

Reflection and standing waves

A rigid barrier reflects an incoming wavefront at an equal and opposite angle to how it arrived, exactly like light off a mirror. Send a wave straight at a wall and the reflected wave travels back through the incoming one; where the two happen to be perfectly out of step they cancel completely at fixed points called nodes, and where they reinforce you get points of maximum motion, antinodes - a standing wave, the pattern that also governs how a guitar string or an organ pipe vibrates.

Frequently asked questions

What is a ripple tank actually used to demonstrate?

A ripple tank is a shallow tray of water with a light shining through it, used to make the behaviour of waves visible from above: reflection off barriers, refraction over depth changes, diffraction through gaps, and interference between two or more sources. Because water waves are slow and large enough to see directly, the tank makes abstract wave equations into something you can watch happen.

Why do waves bend when they enter shallower water?

Shallow-water wave speed is proportional to the square root of the depth, so a wave front slows down as it crosses into shallower water. If the front approaches the depth change at an angle, the part of the wave still in deep water keeps moving faster than the part already in shallow water, and the whole front bends toward the direction of decreasing depth, exactly as light refracts entering a denser medium.

Why does a narrow gap diffract waves more than a wide one?

Diffraction is most noticeable when the gap width is comparable to or smaller than the wavelength, because then the whole opening acts like a single point source radiating outward in near-circular wavefronts, by Huygens' principle. A gap much wider than the wavelength lets most of the wave pass through with its shape largely intact, and only the edges show visible bending.

Try it live

Everything above runs in your browser - open Ripple Tank and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.

▶ Open Ripple Tank simulation

The Ripple Tank: Watching the Wave Equation from Above